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GrizzlyChicken

  • 2 years ago

how do you solve 16^(-3/4) without a calculator?

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  1. 009infinity
    • 2 years ago
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    split the powers and then do individually

  2. GrizzlyChicken
    • 2 years ago
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    what do you mean by split the powers?

  3. 009infinity
    • 2 years ago
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    do u got it

  4. GrizzlyChicken
    • 2 years ago
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    no, im lost where -3 is multiplyed by 6 and then the ^1/4 part

  5. 009infinity
    • 2 years ago
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    ok i explain in steps

  6. theEric
    • 2 years ago
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    (-3) means \[\frac{1}{16^3}\] and (1/4) means \[\sqrt[4]{16}\] right? So, since you're doing both to the 16... it can be written as \[\frac{1}{\sqrt[4]{16^3}}\] or \[\frac{1}{\sqrt[4]{16}^3}\]

  7. GrizzlyChicken
    • 2 years ago
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    that makes sense so far

  8. theEric
    • 2 years ago
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    Now, one looks much more easy to solve than the other, even though they are the same thing.

  9. 009infinity
    • 2 years ago
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    the power is -3/4 base is 16 now 16^-3 . 16^1/4=1/(16)^3.\[\sqrt[4]{16}\]

  10. GrizzlyChicken
    • 2 years ago
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    how does \[\sqrt[4]{16^3}\] turn into 8?

  11. GrizzlyChicken
    • 2 years ago
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    i know the answer is 1/8

  12. GrizzlyChicken
    • 2 years ago
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    \[\sqrt[4]{4096}\]

  13. GrizzlyChicken
    • 2 years ago
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    nvm

  14. theEric
    • 2 years ago
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    I would look at it the other way - just to avoid that huge number \[16^3\].

  15. theEric
    • 2 years ago
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    \[\frac{1}{\sqrt[4]{16}^3}\]

  16. theEric
    • 2 years ago
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    So it's like \[\frac{1}{(\sqrt[4]{16})^3}\]

  17. theEric
    • 2 years ago
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    And what is \[\sqrt[4]{16}\]?

  18. theEric
    • 2 years ago
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    Guess :P

  19. theEric
    • 2 years ago
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    It's a nice number.

  20. GrizzlyChicken
    • 2 years ago
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    2

  21. GrizzlyChicken
    • 2 years ago
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    sorry, i was afk for a while

  22. GrizzlyChicken
    • 2 years ago
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    then 2^3 is 8

  23. GrizzlyChicken
    • 2 years ago
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    so 1/8

  24. GrizzlyChicken
    • 2 years ago
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    thanks!

  25. theEric
    • 2 years ago
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    Understood! Thank you! And you're welcome!

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